1. Field of the Invention
This invention is directed to an exhaustive, deterministic method of searching for and optimizing loading patterns that satisfy designated constraints for a given inventory of fuel assemblies in a nuclear reactor core.
2. Background Information
The core of a nuclear reactor is formed by scores of elongated, rectangular fuel assemblies arranged in a cylindrical vessel. It is common to combine fuel assemblies from previous fuel cycles with new fuel. Thus, a typical inventory of fuel assemblies can be made up of about one-third new, or feed fuel assemblies, about one-third once burned fuel assemblies and about one-third twice burned fuel assemblies. While fuel assemblies within these broad categories will have similar gross characteristics, even among fuel assemblies with a common history there were differences that must be taken into account. To further complicate the problem, a number of different arrangements of burnable absorbers are placed in the feed fuel assemblies to moderate their reactivity.
The arrangement of the fuel assemblies in a loading pattern must meet certain engineering requirements, one of the most important of which is the distribution of power, including limits on power peaks within the core. Another important consideration is maximization of the fuel cycle, or the time required between refuelings.
Historically, one of two techniques has been employed to establish a suitable fuel assembly loading pattern for a reactor core. In one technique, a sequence of random shuffles of fuel assemblies is used to find a loading pattern that meets specified engineering requirements. In the other historical technique, expert rules are used to establish a suitable loading pattern. Neither of these techniques assures the establishment of an optimal loading pattern.
A more analytical approach was suggested in a paper entitled “Mixed Integer Programming for Pressurized Water Reactor Fuel-Loading-Pattern Optimization”, by Taek Kyum Kim and Chang Hyo Kim, published in Nuclear Science and Engineering: 127, 346-357 (1997). This technique begins by assuming an arbitrary initial reference loading pattern of the individual fuel assemblies. The number of possible loading patterns that could be generated by shuffling all of these individual fuel assemblies is formidable. Hence, it is not practical to individually evaluate each possible loading pattern discretely. In order to reduce the processing required, the problem is expressed as a continuous function that can then be differentiated to obtain an optimum solution. This is accomplished by linearizing the relationship between the physical distribution of the fuel assemblies and the pertinent engineering requirements using a generalized perturbation technique. Mixed integer linear programming incorporating branching and bounding is then implemented to determine the optimum loading pattern. As the linearization to individual fuel assemblies can introduce significant error, there is no assurance that the “optimal” loading pattern identified is in fact optimal. Accordingly, the process is repeated using the solution generated by the previous integration. There is no guarantee that subsequent solutions will converge or even that a better loading pattern will be found. The process is also heavily dependent on the initial loading pattern used.
Another method of establishing a fuel assembly loading pattern is described in the paper entitled “Integer Permutation Programming in a Loading Pattern Optimization Code SUPERLPOS Used at SNERDI” presented by Shengyic Si, one of the present inventors, at the PHYSOR 2002 Conference at Seoul, Korea on Oct. 7-10, 2002. This technique involves a two part process. First, the fuel assemblies for a load are grouped into batches based upon initial enrichment and depletion history. For instance, all of the feed fuel assemblies are considered one batch, the once burned fuel assemblies form a second batch, and the twice burned fuel assemblies make up the third batch. Initially, all of the fuel assemblies in each batch are considered to be identical. An enumeration program sequentially generates batch loading patterns one by one by shuffling the batches of fuel assemblies. For each enumerated batch loading pattern the reactivities of the individual fuel assemblies are utilized in the linearization of the effect of fuel assembly position on the specified engineering requirements. Again, mixed integer linear programming incorporating branching and bounding is applied to identify an optimal load pattern of individual fuel assemblies for the selected batch pattern. The second part of the technique is similar to the previously described technique, except that the linearization using the same generalized perturbation technique has smaller errors due to the smaller perturbations required with shuffling individual assemblies inside a batch. In accordance with this technique, different batch loading patterns are serially enumerated and processed to find the optimal daughter loading pattern for each batch loading pattern. A final loading pattern is then manually selected from all of the optimal daughter loading patterns that a user cares to generate.
While this latter technique is an improvement, it still has limitations. First, it does not identify the size of the problem, in that batch loading patterns are serially enumerated and processed. Also, by going directly from the batch groupings to the individual fuel assemblies in one step, there can be wasted time processing patterns that have a dead end where none of the daughter loading patterns meet the specified engineering requirements. Second, going to the individual fuel assemblies in one step, even though the differences are not so large between fuel assemblies in the same batch, still produces sizeable errors in the linearization.
There is room, therefore, for an improved method for establishing loading patterns for nuclear reactor cores.